Your door hinge needs to be rebuilt, there are kits available that either replace the pin with an oversize one or a combination of bushings and new pins. It is not a bad job but getting the door off, the hinge removed and taken apart is not easy.
It appears that your cab is sitting on the frame in your first picture, there should be approximately 3/4" space between them so something is collapsed.
The front cab bolts come through the floor inboard of the cowl area, depending on what you have on the floor they should ebcome obvious once you get down to the metal floor. The front cab mounts consist of a channel formed steel piece attached to the underside of the floor that basically sits on a bracket that is part of the frame (as shown in your last picture).
The splash guard you are seeing may be the guard that is in front of the battery to protect it. It is not part of the cab mounting system.
If your floor is pushed up into the cab interior by the front cab mount the cab is basically sinking around the front cab mount.
